Weak signal detection based on underdamped stochastic resonance with an exponential bistable potential

Stochastic resonance (SR) is a vital approach to detect weak signals submerged in strong background noise, which is useful for mechanical fault diagnosis. The underdamped bistable SR (UBSR) is a kind of the most used SR, however, their potential structures are deficient to match with the complicated and diverse mechanical vibration signals and their parameters are selected subjectively which probably resulting in poor performance of UBSR. To overcome these shortcomings, this paper proposes an underdamped SR with exponential potential (UESR) which is generalized by using a harmonic model and a Gaussian potential (GP) model. The dynamics in UESR system is evaluated by the signal-to-noise ratio (SNR) which represents the effectiveness of noise utilization. Then, the effects of system parameters on system performance are investigated by output SNR versus noise intensity D for different parameters. Finally, the proposed method is used to process bearing experimental data and further perform bearing fault diagnosis. The experimental results demonstrate that a larger output SNR and higher spectrum peaks at fault characteristic frequencies can be obtained by the proposed method compared with the UBSR method, which confirm the effectiveness of the proposed method.     

Solvent relaxation of fluorescent labels as a new tool for the detection of polarity and rigidity changes in membranes

Since solvent relaxation (SR) exclusively depends on the physical properties of the dye environment, SR spectroscopy of defined located labels in amphiphilic assemblies accomplishes the characterisation of specific domains. The most accurate way to characterise SR is the determination of the time-dependent Stokes shift. The time course of the Stokes shift, expressed as a solvent relaxation time, gives information about both the rigidity and polarity of the dye environment. The absolute value of the Stokes shift following the excitation is correlated with the polarity of the probed region. The validity of this approach for the investigation of phospholipid bilayers is illustrated by listing the parameters influencing the SR kinetics of appropriate membrane labels: membrane curvature, percentage of phosphatidylserine (PS) in small unilamell vesicles (SUV), addition of Ca²⁺ ions, binding of vitamin-K dependent proteins, percentage of diether-lipids in phosphatidylcholine (PC)-vesicles, and temperature. Presented at the Czech-Israeli-German Symposium “Dynamical Processes in Condensed Molecular Systems”, Prague, Czech Republic, 26–30 May 1997.     

Time‐differential radio‐frequency muon spin resonance (TD‐RFμSR) technique at a pulsed muon beam

Longitudinal‐field μSR methods, e.g., radio‐frequency μ⁺ spin resonance (RFμSR), are well suited to investigate dynamic processes that destroy the phase coherence of the muon spin ensemble. Additional information on relaxation processes of the muon species under investigation is obtained from time‐differential (TD) data acquisition. In this paper we describe the set‐up of a TD‐RFμSR spectrometer installed at the ISIS pulsed muon facility at the Rutherford Appleton Laboratory (RAL, Chilton, UK). As an example, results of TD‐RFμSR measurements on muons in diamagnetic environment μ^d in a boron‐doped silicon sample under illumination at 55 K are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

A novel parameter-induced adaptive stochastic resonance system based on composite multi-stable potential model

Stochastic resonance (SR) is used widely as a weak signal detection method by using noise in many fields. In order to improve the weak signal processing capability of SR, a novel composite multi-stable model is proposed, which is constructed by the joint of the tristable model and the Gaussian Potential (GP) model. The SR system based on this model is constructed and the signal-to-noise ratio (SNR) is regarded as the index to measure the SR effect. The differential brain storm optimization (DBSO) algorithm is used to optimize the system parameters collaboratively to achieve parameter-induced adaptive SR. The influences of the system parameters V and R and the noise intensity D on the output response of SR system are analyzed under Gaussian white noise and α stable noise environments, and the advantages of the composite multi-stable SR system over the traditional tristable system are verified. For different levels of weak signals, the output performances of SR systems based on composite multi-stable model, traditional tristable model, composite tristable model are compared and analyzed. The results prove that the proposed model has better performance. Meanwhile, the adaptive detection of the multiple high-frequency weak signal is realized using the composite multi-stable SR system. The simulation results show that the proposed system has strong weak signal processing capability and good immunity to noise types, which widens the application range of SR in practical engineering.     

Spatial correlation study of internal magnetic fields in magnets by μSR2-technique

It is shown that using position-sensitive detectors in μSR experiments to determine the muon stopping site in a target permits one to study correlation effects in μSR time histograms produced by the decay of muons stopping in the same domain, i.e. to obtain time correlators of μSR histograms of decays from a small region. These correlators contain information on the spatial correlation of magnetic fields in the sample under study. The proposed method (μSR²-technique) allows measuring correlation radii (r _c ) down to 10⁻⁵ cm in a bulk sample. Among interesting physical phenomena occuring overr _c≥3×10⁻⁶ cm are, for instance, long wavelength fluctuations of the order parameter near the phase transition point in ferromagnets and antiferromagnets and magnetic field correlations in magnet domains and spin glasses. One may use this method also on heavy-current accelerators producing pulsed muon beams to investigate the variation in time of spatial correlations in magnets, spin glasses and superconductors.     

Radio-frequency muon spin resonance (RFμSR) experiments on condensed matter

In this paper we present an overview of the radio-frequency muon spin resonance (RFμSR) technique, an analogue to continuous-wave NMR, and an introduction to time-integral (TI) and time-differential (TD) RFμSR on muons in diamagnetic or in paramagnetic environments. The general form of the resonance line for TI-RFμSR as well as the expression for the time-dependence of the longitudinal muon spin polarization at resonance are given. Since RFμSR does not require phase coherence of the muon spin ensemble, this technique allows us to investigate muon species that are generated by transitions from, or in the course of reactions of, a precursor muon species even if in transverse-field (TF) μSR measurements the signal is lost due to dephasing. This ability of RFμSR is clearly demonstrated by measurements on doped Si. In this example, at low temperatures, a very pronounced signal from a muon species in diamagnetic environment has been found in RFμSR measurements, whereas in TFμSR experiments only a very small signal from muons in diamagnetic environment could be detected and a large fraction of the implanted muons escaped detection. These findings could be interpreted in terms of the delayed formation of a diamagnetic muonium-dopant complex, and, due to the large diamagnetic RFμSR signal, the RFμSR technique is a unique tool to study how the variation of parameters and experimental conditions such as illumination affects formation and behavior of these complexes. First results obtained on illuminated boron doped Si are reported. However, as illustrated by the example of experiments on the muonated radical in solid C₆₀, results from conventional TI-RFμSR cannot always be interpreted unambiguously since different parameters, namely the fraction of muons forming the investigated muon species, the longitudinal and the transverse relaxation rates, have similar effects on height and shape of the RFμSR resonance line. These ambiguities, however, may be resolved by collecting time-differential data. With this extension RFμSR becomes a very powerful complementary method to TFμSR in the studies of dynamic effects.     

Longitudinal field muon spin relaxation (LF-μSR) measurements and evidence for a new muonium defect site in type Ia diamond

A new configuration for muonium, with hyperfine interaction parameters of less than axial symmetry, in nitrogen rich diamond is identified in Longitudinal Field Muon Spin Relaxation (LF-μSR) measurements. The TF-μSR measurements on the same sample show that almost the entire strength of the new configuration is accounted for by a “missing fraction”, typically seen in nitrogen rich type Ia diamond. The “missing fraction” is therefore the result of a T2 relaxation. This is consistent with muon trapping at or in some nitrogen related defect(s) followed by electron capture at random times. This revised version was published online in August 2006 with corrections to the Cover Date.     

Adaptive bistable stochastic resonance and its application in mechanical fault feature extraction

Stochastic resonance (SR) is an important approach to detect weak vibration signals from heavy background noise. In order to increase the calculation speed and improve the weak feature detection performance, a new bistable model has been built. With this model, an adaptive and fast SR method based on dyadic wavelet transform and least square system parameters solving is proposed in this paper. By adding the second-order differential item into the traditional bistable model, noise utilization can be increased and the quality of SR output signal can be improved. The iteration algorithm for implementing the adaptive SR is given. Compared with the traditional adaptive SR method, this algorithm does not need to set up the searching range and searching step size of the system parameters, but only requires a few iterations. The proposed method, discrete wavelet transform and the traditional adaptive SR method are applied to analyzing simulated vibration signals and extracting the fault feature of a rotor system. The contrastive results verify the superiority of the proposed method, and it can be effectively applied to weak mechanical fault feature extraction.     

The positive muon as a probe in magnetism

The special features of the Muon Spin Rotation (μSR) method for investigation of magnetic materials are discussed. The positive muon is a probe which is very sensitive to small magnetic fields at the interstitial site where the muon comes to rest. Some of the basic aspects of μSR and examples of its application in magnetic studies are presented.     

Stochastic resonance in extended systems

Here, three highly nontrivial instances are briefly discussed, showing both the degree of maturity achieved by the field of stochastic resonance (SR) and the wealth of potential realizations of SR in extended systems: (1) a “bound” KPZ system, for which the knowledge of its nonequilibrium potential (NEP) makes simple the solution of a very complex problem; (2) the Ising-Bloch front bifurcation in an activator-inhibitor system, a case of SR between moving fronts of opposite chirality; (3) a spatiotemporally chaotic “toy model”, useful for climate research, exhibiting internal SR due to chaos suppression.     

RF resonance techniques for continuous muon beams

RF excitation was first used in μSR in 1958 [1]. However, even with the advent of modern meson facilities the use of RF techniques in μSR has not flourished, in part due to the muon's short lifetime, but mainly because unlike NMR RF fields are simply not used to detect the muon's polarization. Nevertheless, a cursory survey of the relative power and sophistication of these two related fields leaves little doubt that the pursuit of RF resonance within μSR will add significantly to its analytical capability. At TRIUMF over the past few years we have worked toward developing RF capabilities suitable for use in a CW meson facility. Several spectroscopic applications utilizing time integral techniques have been tested. These include detection of final states in semiconductor and substituted radical systems, the very pretty two photon absorption (TPA) experiments, and the use of low field swept frequency excitation to measure nuclear hyperfine parameters in Mu like system. Of course, the most celebrated use of RF in magnetic resonance is its application to spin dynamics via various spin echo techniques. The adaptation of the spin echo to μSR is discussed and examples of both transverse and longitudinal field echoes are presented.     

High pressure μSR studies: rare earths and related materials

After a short introduction to μSR with respect to the study of magnetic properties, followed by a brief outline of the principle of the high pressure-low temperature μSR spectrometer installed at the Paul Scherrer Institute, we discuss some measurements on rare earth materials employing this instrument. They are concerned with: (1) The pressure dependence of the spin turning process in ferromagnetic Gd. (2) The volume dependence of the internal magnetic field in the heavy rare earth metals Gd, Dy, and Ho in their ordered magnetic states. (3) The response of the (first order) magnetic transition in the frustrated antiferromagnets of type RMn₂ (R = Y,Gd) to pressure. (4) The variation of magnetic parameters with pressure in La₂CuO₄ (powder sample), the antiferromagnetic parent compound of the high T_C superconductors of type La_2−x(Sr, Ba)_xCuO₄. In conclusion a short outlook on further developments is given. This revised version was published online in July 2006 with corrections to the Cover Date.     

Stochastic resonance in a bistable system with global delay and two noises

The global time delay is introduced into a bistable system driven by two noises and a periodic signal. The signal power amplification factor η is employed to characterise stochastic resonance (SR) of the system. Numerical simulation results indicate the following. (1) For a periodic signal with low frequency (Ω), the typical behaviour of the SR is lowered monotonically by increasing the delay time τ; for moderate Ω, τ enhances the SR behaviour and then weakens it, with a critical value at which the SR is optimum. (2) Multiplicative noise intensity D and additive noise intensity α have different influences on the SR performance, viz D enhances the SR monotonically while α enforces the SR initially and then restrains it; (3) correlation intensity λ between the two noises always weakens the SR behaviour of the system.     

Quantitative assessment of effects of phase aberration and noise on high-frame-rate imaging

The goal of this paper is to quantitatively study effects of phase aberration and noise on high-frame-rate (HFR) imaging using a set of traditional and new parameters. These parameters include the traditional −6-dB lateral resolution, and new parameters called the energy ratio (ER) and the sidelobe ratio (SR). ER is the ratio between the total energy of sidelobe and the total energy of mainlobe of a point spread function (PSF) of an imaging system. SR is the ratio between the peak value of the sidelobe and the peak value of the mainlobe of the PSF. In the paper, both simulation and experiment are conducted for a quantitative assessment and comparison of the effects of phase aberration and noise on the HFR and the conventional delay-and-sum (D&S) imaging methods with the set of parameters. In the HFR imaging method, steered plane waves (SPWs) and limited-diffraction beams (LDBs) are used in transmission, and received signals are processed with the Fast Fourier Transform to reconstruct images. In the D&S imaging method, beams focused at a fixed depth are used in transmission and dynamically focused beams are used in reception for image reconstruction.The simulation results show that the average differences between the −6-dB lateral beam widths of the HFR imaging and the D&S imaging methods are −0.1337 mm for SPW and −0.1481 mm for LDB, which means that the HFR imaging method has a higher lateral image resolution than the D&S imaging method since the values are negative. In experiments, the average differences are also negative, i.e., −0.2804 mm for SPW and −0.3365 mm for LDB. The results for the changes of ER and SR between the HFR and the D&S imaging methods have negative values, too. After introducing phase aberration and noise, both simulations and experiments show that the HFR imaging method has also less change in the −6-dB lateral resolution, ER, and SR as compared to the conventional D&S imaging method. This means that the HFR imaging method is less sensitive to the phase aberration and noise.Based on the study of the new parameters on the HFR and the D&S imaging methods, it is expected that the new parameters can also be applied to assess quality of other imaging methods.     

A novel piecewise tri-stable stochastic resonance system with time-delayed feedback and its application

It is of great significance to judge whether mechanical equipment has faults, so it is necessary to study the extraction of mechanical fault characteristic signals. Stochastic resonance (SR) has been applied diffusely in feature extraction because of its excellent output performance, but there are few studies on SR with time-delay feedback (TF) terms. In some cases, the output of the system will be improved when the TF term is added to the SR system, so it is meaningful to study the SR with TF term. Because piecewise tri-stable system has good characteristics of overcoming output saturation, on the basis of piecewise tri-stable SR (PTSR), the time-delay feedback PTSR (TFPTSR) is proposed, and for purpose of further studying the internal mechanism of this system, its generalized potential function and the law that the parameter causes its change are derived and studied. Then the probability density function (PDF) of the proposed model and its mean first-passage time (MFPT) are calculated and compared with the variation of the generalized potential function together with the Signal to noise ratio (SNR), through such research, the difficulty of the system to produce stochastic resonance and the degree of the output performance are directly related to the system parameters. Finally, the proposed TFPTSR method processes the same signal as the PTSR method, and it is found that the TFPTSR method can get better output SNR.     

An improved multiscale noise tuning of stochastic resonance for identifying multiple transient faults in rolling element bearings

Stochastic resonance (SR), a noise-assisted tool, has been proved to be very powerful in weak signal detection. The multiscale noise tuning SR (MSTSR), which breaks the restriction of the requirement of small parameters and white noise in classical SR, has been applied to identify the characteristic frequency of a bearing. However, the multiscale noise tuning (MST), which is originally based on discrete wavelet transform (DWT), limits the signal-to-noise ratio (SNR) improvement of SR and the performance in identifying multiple bearing faults. In this paper, the wavelet packet transform (WPT) is developed and incorporated into the MSTSR method to overcome its shortcomings and to further enhance its capability in multiple faults detection of bearings. The WPT-based MST can achieve a finer tuning of multiscale noise and aims at detecting multiple target frequencies separately. By introducing WPT into the MST of SR, this paper proposes an improved SR method particularly suited for the identification of multiple transient faults in rolling element bearings. Simulated and practical bearing signals carrying multiple characteristic frequencies are employed to validate the performance improvement of the proposed method as compared to the original DWT-based MSTSR method. The results confirm the good capability of the proposed method in multi-fault diagnosis of rolling element bearings.     

Muon bonding versus muonium formation: Muon-Spin-Relaxation in α-Al2O3

Results of Muon-Spin-Relaxation (μSR) experiments on well-defined single crystals of corundum (α-Al₂O₃) are reported. Major issue in this study is the controversy of muon bonding or muonium formation in insulators. Transverse, zero-field and longitudinal field measurements were performed as a function of temperature or applied field. The obtained results indicate that muon-oxygen bonding occurs in α-Al₂O₃, having (at least) two (μO) states as found earlier for α-Fe₂O₃. The occurrence of a 10% missing fraction suggests Mu states, although Mu was not observed in our measurements. These results and their implications are discussed in light of other experimental μSR studies on insulating oxides and the above-mentioned controversy.     

Effects of combined harmonic and random excitations on a Brusselator model

We discuss the constructive role of combined harmonic and random excitation on stochastic resonance (SR) in a Brusselator model. We first numerically investigate SR determined by the Signal-to-Noise Ratio (SNR) in this model. Effects of different parameters on SR are described in detail. Our simulation results show that the intensity of the Gaussian colored noise and the amplitude of the periodic force can enhance SR. Moreover, an analytical framework is presented for the SNR of the Brusselator model, leading to a theoretical expression of SNR. We observe a good agreement between the theoretical and numerical results, and the effectiveness of the proposed theoretical method is verified. This theoretical analysis provides a global view on how the dynamics of a periodically forced system with noise changes in the vicinity of a Hopf bifurcation.     

Stochastic resonance induced by a multiplicative periodic signal in a logistic growth model with correlated noises

The stochastic resonance (SR) phenomenon induced by a multiplicative periodic signal in a logistic growth model with correlated noises is studied by using the theory of signal-to-noise ratio (SNR) in the adiabatic limit. The expressions of the SNR are obtained. The effects of multiplicative noise intensity α and additive noise intensity D, and correlated intensity λ on the SNR are discussed respectively. It is found that the existence of a maximum in the SNR is the identifying characteristic of the SR phenomena. In comparison with the SR induced by additive periodic signal, some new features are found: (1) When SNR as a function of λ for fixed ratio of α and D, the varying of α can induce a stochastic multi-resonance, and can induce a re-entrant transition of the peaks in SNR vs λ; (2) There exhibits a doubly critical phenomenon for SNR vs D and λ, i.e., the increasing of D (or λ) can induce the critical phenomenon for SNR with respect to λ (or D); (3) The doubly stochastic resonance effect appears when α and D are simultaneously varying in SNR, i.e., the increment of one noise intensity can help the SR on another noise intensity come forth.